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The consolidation of unsaturated soil is of great significance to road engineering, soft foundation soil improvement, etc. Based on the one-dimensional consolidation theory of unsaturated soil proposed by Fredlund and Hasan, the governing equations for pore water pressure and pore air pressure in the soil are established. The initial conditions and a type of time-dependent mixed nonhomogeneous boundary conditions of single-layer unsaturated soil are presented which constitutes the solution of 1D consolidation of unsaturated soil. The homogenization of nonhomogeneous boundary conditions and the eigenfunction expansion method are adopted to derive exact analytical solutions in time domain for the dissipation of pore water pressure and pore air pressure in the soil. Finally, the method proposed in this paper is validated by comparison with published results, and several examples are used to analyze the effects of exponentially changing boundary conditions on the dissipation of pore water pressure, pore air pressure, and deformation of unsaturated soils. The results show that the speed of exponential change of pore pressure on the boundary or flux across the boundary has significant effect on the consolidation process of unsaturated soil.